Similar to the proof in [1]} (see its Section 9.2.2 for details), it is easy to show that \(\lambda \)  in the AS algorithm is the slope of the RD curve, which corresponds to the annealing parameter in the BA algorithm.
Specifically, the AS algorithm updates the dual variable \(\lambda \)  in every iteration by Newton's method with only a few steps since we observe the nice monotonic property of \(G(\lambda )\)  in (REF ).
On the other hand, the BA algorithm fixes its parameter \(\lambda \)  as a constant throughout the iterations. Hence it cannot compute the rate \(R\)  directly for a given distortion \(D\) .
